# What is a solution to the differential equation dy/dx=2x?

Jul 15, 2018

$y = {x}^{2} + C$

#### Explanation:

Writing

$\mathrm{dy} = 2 x \mathrm{dx}$
and integrating we get

$y = {x}^{2} + C$
This equation is separable.

Jul 15, 2018

$y = {x}^{2} + C$

#### Explanation:

Let's get a $\mathrm{dx}$ on the right so we can integrate. This can be done by multiplying both sides by $\mathrm{dx}$. We now have

$\mathrm{dy} = 2 x \mathrm{dx}$

If we have

$f ' \left(x\right) = g \left(x\right)$, then this means $f \left(x\right) = \int g \left(x\right) \mathrm{dx}$

Our $f ' \left(x\right)$ is essentially $\mathrm{dy}$ and our $g \left(x\right) = 2 x$. We now have

$y = \int 2 x \mathrm{dx}$

Integrating with the reverse power rule, we get

$y = {x}^{2} + C$

Hope this helps!